Keep in mind you will only be able to see this information if the buying organization has this feature enabled.

The Document Takers list allows you to see exactly who has downloaded the Public Files and generates them based on existing documents that are available on a project.

If a Project Owner deletes a document or deletes and re-uploads a new version of a document, anyone who had downloaded the original document will no longer appear on the Document Takers list as that document no longer exists within the context of their Project.